Vol. 316, No. 1, 2022

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Powers of sums and their associated primes

Hop D. Nguyen and Quang Hoa Tran

Vol. 316 (2022), No. 1, 217–235

Let A and B be polynomial rings over a field k, and let I A and J B be proper homogeneous ideals. We analyze the associated primes of powers of I + J A kB given the data on the summands. The associated primes of large enough powers of I + J are determined. We then answer positively a question due to I. Swanson and R. Walker about the persistence property of I + J in many new cases.

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associated prime, powers of ideals, persistence property
Mathematical Subject Classification
Primary: 13A15, 13F20
Received: 6 March 2021
Revised: 26 June 2021
Accepted: 5 November 2021
Published: 26 February 2022
Hop D. Nguyen
Institute of Mathematics
Quang Hoa Tran
University of Education
Hue University